# Help with checking Vector Question

#### mathematicallyretarded

Hey guys I am not sure if i am on the right track here so i need some advice

Question is:

if $$\displaystyle \vec{a}=3i-2j$$ , $$\displaystyle \vec{b}=-4i+4j$$ , and $$\displaystyle \vec{c}=6i+-9j$$ express the following vectors in their simplest form:

(i)$$\displaystyle -5\vec{b}$$
(ii)$$\displaystyle 2\vec{a}-\frac{1}{2}\vec{c}$$
(iii)$$\displaystyle \frac{2}{3}\vec{a}-\frac{1}{2}\vec{b}-\frac{1}{4}\vec{c}$$

My Solution:

(i) $$\displaystyle -5\left(-4i+4j \right)=20i+\left(-20j \right)$$
(ii) $$\displaystyle 2(3i-2j)-\frac{1}{2}(6i+(-9)j)$$
$$\displaystyle = 6i-4j-3i+(-\frac{9}{2})j$$
$$\displaystyle = (6-3=3i) -4j-\frac{9}{2}$$
$$\displaystyle = -\frac{4}{1}-\frac{9}{2}$$
$$\displaystyle =-\frac{8}{2}-\frac{9}{2}$$
$$\displaystyle =-\frac{17}{2}$$

Answer? $$\displaystyle 3i-\frac{17}{2}j$$

(iii) $$\displaystyle \frac{2}{3}(3i-2j)-\frac{1}{2}(-4i+4j)-\frac{1}{4}(6i+(-9)j)$$
$$\displaystyle (2i-\frac{4}{3}j)-(-2i+2j)-(\frac{3}{2}i+(-\frac{9}{4}j)$$
$$\displaystyle 2i+2i-\frac{3}{2}i$$
$$\displaystyle = \frac{4}{1}i+\frac{3}{2}i$$
$$\displaystyle = \frac{8}{2}+\frac{3}{2}$$
$$\displaystyle =\frac{11}{2}i$$

$$\displaystyle -\frac{4}{3}j+\frac{2}{1}j-\frac{9}{4}j$$
$$\displaystyle = -\frac{16}{12}j+\frac{24}{12}j-\frac{27}{12}j$$
$$\displaystyle = -\frac{19}{12}j$$

Answer? $$\displaystyle \frac{11}{2}i-\frac{19}{12}j$$

#### sa-ri-ga-ma

while removing the brackets, you have to follow the following rule.

-2(a-b) = -2a + 2b

-2(a+b) = -2a - 2b

Therefore your second the third problems are wrong. Correct it.

#### mathematicallyretarded

while removing the brackets, you have to follow the following rule.

-2(a-b) = -2a + 2b

-2(a+b) = -2a - 2b

Therefore your second the third problems are wrong. Correct it.
ok so (ii) answer is $$\displaystyle 3{\bf i}+(-4+\frac{9}{2}){\bf j}=3{\bf i}+\frac{1}{2}{\bf j}$$

now i will do the (iii) one again

#### mathematicallyretarded

Ok would the (iii) one be

$$\displaystyle \frac{5}{2}i+\frac{7}{6}j$$

#### Soroban

MHF Hall of Honor
Hello, mathematicallyretarded!

You are making hard work out of it.

This is basically Algebra I . . . combining like terms.

Given: .$$\displaystyle \begin{array}{ccc}\vec a &=&3i-2j \\ \vec b &=&-4i+4j \\ \vec c &=&6i-9j\end{array}$$

Express the following vectors in their simplest form:

$$\displaystyle (i) \;-5\vec{b}$$

$$\displaystyle -5\vec b \;\;=\;\;-5(-4i + 4j) \;\;=\;\;20i - 20j$$

$$\displaystyle (ii) \;\;2\vec a -\tfrac{1}{2}\vec c$$

$$\displaystyle 2\vec a - \tfrac{1}{2}\vec c \;\;=\;\;2(3i - 2j) - \tfrac{1}{2}(6i-9j)$$

. . . . . .$$\displaystyle =\;\;6i - 4j - 3i + \tfrac{9}{2}j$$

. . . . . .$$\displaystyle =\;\;3i + \frac{1}{2}j$$

$$\displaystyle (iii)\;\;\tfrac{2}{3}\vec a -\tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c$$

$$\displaystyle \tfrac{2}{3}\vec a - \tfrac{1}{2}\vec b - \tfrac{1}{4}\vec c \;\;=\;\;\tfrac{2}{3}(3i - 2j) - \tfrac{1}{2}(-4i + 4j) - \tfrac{1}{4}(6i - 9j)$$

. . . . . . . . .$$\displaystyle =\;\;2i - \tfrac{4}{3}j + 2i - 2j - \tfrac{3}{2}i + \tfrac{9}{4}j$$

. . . . . . . . .$$\displaystyle =\;\;\frac{5}{2}i - \frac{13}{12}j$$

#### mathematicallyretarded

Thanks! I have to learn to keep it simple